Turbomachinery and method of manufacturing the same

ABSTRACT

An impeller in a turbomachinery has blades designed such that reduced static pressure difference ΔCp between the hub and the shroud on the suction surface of the blade shows a remarkably decreasing tendency near the impeller exit as it approaches the impeller exit between the impeller inlet and the impeller exit.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is the national stage of International Application No.PCT/GB95/02904 filed Dec. 7, 1995.

TECHNICAL FIELD

The present invention relates to a turbomachinery and a method ofmanufacturing the turbomachinery which includes a centrifugal pump or amixed flow pump for pumping liquid, a blower or a compressor forcompression of gas, and more particularly to a turbomachinery having animpeller which has a fluid dynamically improved blade profile forsuppressing a meridional component of secondary flow, and a method ofmanufacturing such a turbomachinery.

BACKGROUND ART

Conventionally, in flow channels of an impeller in a centrifugal or amixed flow turbomachinery, main flows flowing along the flow channelsare affected by secondary flows generated by movement of low energyfluid in boundary layers on wall surfaces due to static pressuregradients in the flow channels. This phenomenon leads to the formationof streamwise vortices or flows having non-uniform velocity in the flowchannel, which in turn results in a substantial fluid energy loss notonly in the impeller but also in the diffuser or guide vanes downstreamof the impeller.

The secondary flow is defined as a flow which has a velocity componentperpendicular to the main flow. The total energy loss caused by thesecondary flows is referred to as the secondary flow loss. The lowenergy fluid accumulated at a certain region in the flow channel maycause flow separation on a large scale, thus producing a positivelysloped characteristic curve and hence preventing stable operation of theturbomachine.

There is a known approach for suppressing the secondary flows in aturbomachine which is to make the impeller have a specific flow channelgeometry. As an example of such approach using a specific flow channelgeometry, there is a known method in which blades of the impeller in anaxial turbomachine are leaned towards the circumferential directionthereof or the direction of the suction or the discharge side (L. H.Smith and H. Yeh, "Sweep and Dihedral Effects in Axial FlowTurbomachinery", Trans ASME, Journal of Basic Engineering, Vol. 85, No.3, 1963, pp. 401-416), or a method in which blades in a turbine cascadeare leaned or curved toward a circumferential direction thereof (W.Zhongqi, et al., "An Experimental Investigation into the Reasons ofReducing Secondary Flow Losses by Using Leaned Blades in RectangularTurbine Cascades with Incidence Angle", ASME Paper 88-GT-4), or a methodin which a radial rotor has a blade curvature in the spanwise directionwith a convex blade pressure surface and/or a concave blade suctionsurface (GB2224083A). These methods are known to have a favorableinfluence upon the secondary flows in the flow channel if appliedappropriately.

However, since the influence of the profile of a blade camber line or ablade cross-section upon the secondary flow has not been essentiallyknown, the effect of blade lean or spanwise blade curvature is utilizedunder a certain limitation without changing the blade camber line or theblade cross-section substantially. Further, Japanese laid-open PatentPublication No. 60-10281 discloses a structure in which a projectingportion is provided at the corner of a hub surface and a blade surfacein a turbomachine to reduce the secondary flow loss. Since such flowchannel profile is a specific blade profile having a nonaxisymmetric hubsurface, it is difficult to manufacture the impeller.

In all cases of the above prior art, the method of achieving the effectuniversally has not been sufficiently studied. Therefore, the universalmethods of suppressing the secondary flows under different designconditions and for different types of turbomachines have not beenestablished. Under these circumstances, there are many cases that theabove effect is reduced, or to make matters worse, undesirable effectsare obtained.

In general, the three-dimensional geometry of an impeller is defined asa meridional geometry formed by a hub surface and a shroud surface and ablade profile serving to transmit energy to fluid. As the meridionalgeometry, various geometries including a centrifugal type, a mixed flowtype and an axial flow type are selected in accordance with designspecifications, including flow rate, pressure head and rotational speed,which are required in the individual turbomachinery. As a type numbercharacterizing the meridional geometry of an impeller, a specific speedN_(s) =NQ^(1/2) /H^(3/4) (for pumps), is widely used for designing ofthe impeller. Here, N is the rotational speed in revolutions per minute(rpm), Q is the flow rate in cubic meters per minute (m³ /min) and H isthe head in meters (m) representing fluid energy which is imparted tothe fluid by the turbomachinery. That is, the specific speed isdetermined if the design specifications are given, and the meridionalgeometry of the impeller can be suitably selected in accordance with thespecific speed. Incidentally, Q is defined as volume flow rate, and incase of a compressor or the like, the volume flow rate at an impellerinlet is used for a compressible fluid whose volume is variable betweenthe impeller inlet and the impeller exit.

With regard to a blade profile, the inlet blade angle is determined bythe assumed inlet velocity triangle at each spanwise location to matchthe inlet blade angle with the inlet flow angle. On the other hand, theexit blade angle is determined by the assumed exit velocity triangle ateach spanwise location to satisfy the design head. The inlet and theexit velocity triangles are calculated from the meridional geometry andthe design flow rate and the design head, but can be updated based onthe results of flow calculations of the impeller. However, there aremany degrees of freedom as to ways of determining blade angledistribution which controls inlet and exit blade angles, and in effectthe choice of the blade angle distribution is left to designer'sintuition.

There have been proposed up to now many methods in accordance with theapproach which makes the impeller have a specific flow channel geometryto suppress the secondary flows. However, since the method of achievingthe effect universally has not been sufficiently studied, designcriterion of blade profiles having many degrees of freedom has not beenestablished. Therefore, universal methods of suppressing the secondaryflows under different design conditions and for different specificspeeds have not been established. Under these circumstances, thethree-dimensional geometry of the impeller has been designed on thebasis of variation of blade angle distribution of the impeller by trialand error to find the optimum profile of the impeller for suppressingthe secondary flow.

Next, a conventional method of designing the three-dimensional geometryof the impeller on the basis of variation of blade angle distribution bytrial and error will be described below in accordance with a flow chartin FIG. 3(A).

In the first step (step of determining meridional plane), the designspecification is input to determine the meridional geometry and thenumber of blades of the impeller. Next, a plurality of surfaces ofrevolution are defined on a meridional flow passage, and the tangentialcoordinate f₀ of a blade camber line at a point on each of surface ofrevolution is specified based on past experience. The location, wherethe tangential coordinate f₀ is specified, is selected at the leadingedge or at the trailing edge of the impeller in many cases. Thus aspecified location of the tangential coordinate f₀ is referred as thestacking condition.

In the second step (step of determining blade angle distribution), theblade angle at the impeller inlet is determined from the meridionalgeometry of the impeller obtained by the first step and design flowrate. Next, the blade angle at the impeller exit is determined from themeridional geometry of the impeller obtained by the first step, anddesign head. A curve which connects smoothly the determined blade angleat the impeller inlet and the blade angle at the impeller exit isdefined to determine the blade angle distribution along the location ofnon-dimensional meridional distance m.

In the third step (step of determining a blade profile), tangentialcoordinate (wrap angle) of the blade camber line in each of thelocations of non-dimensional meridional distance m is determined byintegrating ∂f/∂m=1/(r tan β) with the location of non-dimensionalmeridional distance m on the basis of blade angle distribution β betweenthe impeller inlet and the impeller exit along each stream line in thelocation of non-dimensional meridional distance m, using stackingcondition f₀ as an initial value. The three-dimensional geometry of theimpeller is determined by adding a certain thickness to the determinedblade camber line to allow the blade to have mechanical strength.

In the fourth step (step of evaluating flow fields), three-dimensionalinviscid flow analysis which is a flow analysis without consideration ofviscosity of fluid is applied to the three-dimensional geometry of theimpeller determined by the third step, and a possibility of poorperformance caused by flow separation due to rapid deceleration of flowin the impeller is evaluated. In the case where it is judged that thepressure distribution in the impeller is not appropriate, after goingback to the second step to modify the blade angle distribution, thesteps from the second step to the fourth step are repeated until theexpected result is achieved.

In case of suppressing the secondary flow by the above-mentionedconventional method of manufacturing the impeller, the followingdisadvantages are enumerated.

(1) In the fourth step, the criteria (including the dependence on thespecific speed of the impeller) for judging whether optimum pressuredistribution in the flow channel is achieved to suppress the secondaryflow is uncertain. Though the state of generation of the secondary flowscan be examined by three-dimensional viscous flow analysis, an enormousamount of calculations is required, thus optimization of the bladeprofile of the impeller by repeating the steps from the second step tothe fourth step is practically not infeasible.

(2) Although it is necessary to make the blade angle distribution properin the second step, if the blade angle distribution which achieves thesecondary flow suppression deviates greatly from conventionalexperience, it is difficult to assume favorable blade angledistribution. Therefore, in practice, it has been difficult to find bytrial and error the optimum blade profile of the impeller forsuppressing secondary flow.

However, recently, as a design method of a blade profile of theimpeller, it is known that if a blade loading distribution is given, thethree-dimensional geometry of the impeller which realizes the givenblade loading distribution can be determined by using athree-dimensional inverse design method which is published in thefollowing literature.

Zangeneh, M., 1991, "A Compressible Three Dimensional Blade DesignMethod for Radial and Mixed Flow Turbomachinery Blades", InternationalJournal of Numerical Methods in Fluids, Vol. 13, pp. 599-624., Borges,J. E., 1990, "A Three-Dimensional Inverse Method for Turbomachinery:Part I--Theory", Transaction of the ASME, Journal of Turbomachinery,Vol. 112, pp. 346-354, Yang, Y. L., Tan, C. S. and Hawthorne, W. R.,1992, "Aerodynamic Design of Turbomachinery Blading in Three-DimensionalFlow: An Application to Radial Inflow Turbines", ASME Paper 92-GT-74,Dang, T. Q., 1993, "A Fully Three-Dimensional Inverse Method forTurbomachinery Blading in Transonic Flows", Transactions of the ASME,Journal of Turbomachinery, Vol. 115, pp. 354-361, Borges, J. E., 1993 "Aproposed Through-Flow Inverse Method for the Design of Mixed-FlowPumps", International Journal for Numerical Methods in Fluids, Vol. 17,pp. 1097-1114.

Most of the above methods design the blade shape based on thethree-dimensional inviscid flow through the blade channels. However, themethod described by Borges (1993) uses a more approximate Actuator Ductapproach in which the flow field is assumed to be axisymmetric. Such anapproximate approach can provide a very computationally efficient meansof arriving at the blade geometry for a specified loading distribution.However, the errors in this approach become quite high for very highlyloaded turbomachines such as centrifugal pumps. Incidentally, in none ofthese literatures has the inverse design method been used for thepurpose of suppression of secondary flows in an impeller.

It is apparent from the secondary flow theory that the secondary flow inthe impeller results from the action of the Coriolis force caused by therotation of the impeller and the effects of the streamline curvature.The secondary flow in the impeller is divided broadly into twocategories, one of which is blade-to-blade secondary flow generatedalong a shroud surface or a hub surface, the other of which is themeridional component of secondary flow generated along the pressuresurface or the suction surface of a blade.

It is known that the blade-to-blade secondary flow can be minimized bymaking the blade profile to be backswept. Regarding the other type ofsecondary flow, that is, the meridional component of secondary flow, itis difficult to weaken or eliminate it easily. If we wish to weaken oreliminate the meridional component of secondary flow, it is necessary tooptimize the three-dimensional geometry of the flow channel verycarefully.

The purpose of the present invention is to suppress the meridionalcomponent of secondary flow in a centrifugal or a mixed flowturbomachine.

As an example of a typical impeller in the turbomachinery to which thepresent invention is applied, the three-dimensional geometry of a closedtype impeller is schematically shown in FIGS. 1(A) and 1(B) in such astate that most of a shroud surface is removed. FIG. 1(A) is aperspective view partly in section, and FIG. 1(B) is a cross-sectionalview taken along a line A-A' which is a meridional cross-sectional view.In FIGS. 1(A) and 1(B), a hub surface 2 extends radially outwardly froma rotating shaft 1 so that it has a curved surface similar to a cornsurface. A plurality of blades 3 are provided on the hub surface 2 sothat they extend radially outward from the rotating shaft 1 and aredisposed at equal intervals in the circumferential direction. The bladetips 3a of the blades 3 are covered with a shroud surface 4 as shown inFIG. 1(B). A flow channel is defined by two blades 3 in confrontationwith each other, the hub surface 2 and the shroud surface 4 so thatfluid flows from an impeller inlet 6a toward an impeller exit 6b. Whenthe impeller 6 is rotated about an axis of the rotating shaft 1 at anangular velocity ω, fluid flowing into the flow channel form theimpeller inlet 6a is delivered toward the impeller exit 6b of theimpeller 6. In this case, the surface facing the rotational direction isthe pressure surface 3b, and the opposite side of the pressure surface3b is the suction surface 3c. In the case of open type impeller, thereis no independent part for forming the shroud surface 4, but a casing(not shown in the drawing) for enclosing the impeller 6 serves as theshroud surface 4. Therefore, there is no basic fluid dynamicaldifference between the open type impeller and the closed type impellerin terms of the generation and the suppression of the meridionalcomponent of secondary flows, thus only the closed type impeller will bedescribed below.

The impeller 6 having a plurality of blades 3 is incorporated as a maincomponent, the rotating shaft 1 is coupled to a driving source, therebyjointly constituting a turbomachine. Fluid is introduced into theimpeller inlet 6a through a suction pipe, pumped by the impeller 6 anddischarged from the impeller exit 6b, and then delivered through adischarge pipe to the outside of the turbomachine.

The unsolved serious problem in connection with the impeller of aturbomachine is the suppression of the meridional component of secondaryflow. The mechanism of generation of the meridional component ofsecondary flow, whose suppression is the purpose of this invention, isexplained as follows:

As shown in FIG. 1(B), with regard to the relative flow, the reducedstatic pressure distribution, defined as p^(*) =p-0.5ρu², is formed bythe action of a centrifugal force W² /R due to streamline curvature ofthe main flow and the action of Coriolis force 2ωW.sub.θ due to therotation of the impeller, where W is the relative velocity of flow, R isthe radius of streamline curvature, ω is the angular velocity of theimpeller, W.sub.θ is the component in the circumferential direction of Wrelative to the rotating shaft 1, p^(*) is reduced static pressure, p isstatic pressure, ρ is density of fluid, us is peripheral velocity at acertain radius r from the rotating shaft 1. The reduced static pressurep^(*) has such a distribution in which the pressure is high at the hubside and low at the shroud side, so that the pressure gradient balancesthe centrifugal force W² /R and the Coriolis force 2ωW.sub.θ directedtoward the hub side.

In the boundary layer along the blade surface, since the relativevelocity W is reduced in the boundary layer developing along the wallsurface, the centrifugal force W² /R and the Coriolis force 2ωW.sub.θacting on the fluid in the boundary layer become small. As a result,they cannot balance the reduced static pressure gradient of the mainflow, and low energy fluid in the boundary layer flows towards an areaof low reduced static pressure p^(*), thus generating the meridionalcomponent of secondary flow. That is, as shown in broken lines on thepressure surface 3b and in solid lines on the suction surface 3c in FIG.1(A), fluid moves along the blade surface from the hub side towards theshroud side on the pressure surface 3b and the suction surface 3cforming meridional component of secondary flow.

The meridional component of secondary flow is generated on both surfacesof the suction surface 3c and the pressure surface 3b. In general, sincethe boundary layer on the suction surface 3c is thicker than that on thepressure surface 3b, the secondary flow on the suction surface 3c has agreater influence on performance characteristics of turbomachinery. Thepurpose of the present invention is to suppress the meridional componentof secondary flow in the suction surface of the blade.

When low energy fluid in the boundary layer moves from the hub side tothe shroud side, fluid flow is formed from the shroud side to the hubside at around the midpoint location to compensate for fluid flow ratewhich has moved. As a result, as shown schematically in FIG. 2(B) whichis a cross-sectional view taken along a line B-B' in FIG. 2(A), a pairof vortices which have a different swirl direction from each other areformed in the flow channel between two blades as the flow goes towardsexit. These vortices are referred to as secondary vortices. Low energyfluid in the flow channel is accumulated due to these vortices at acertain location of the impeller towards the exit where the reducedstatic pressure p^(*) is lowest, and this low energy fluid is mixed withfluid which flows steadily in the flow channel, resulting in generationof a great flow loss.

Furthermore, when the non-uniform flow generated by insufficient mixingof a low relative velocity (high loss) fluid and a high relativevelocity (high loss) fluid is discharged to the downstream flow channelof the blades, a great flow loss is generated when both fluids aremixed.

Such a non-uniform flow leaving the impeller makes the velocity triangleunfavorable at the inlet of the diffuser and causes flow separation ondiffuser vanes or a reverse flow within a vaneless diffuser, resultingin a substantial decrease of the overall performance of theturbomachine.

Furthermore, in the area of high loss fluid accumulated at a certainlocation in the flow channel, a large scale reverse flow is liable tooccur, thus producing a positively sloped characteristics curve. As aresult, surging, vibration, noise and the like are generated, and theturbomachinery cannot be stably operated especially at partial flowrate.

Therefore, in order to improve the performance of centrifugal or mixedflow turbomachinery and realize stable operation of turbomachinery, itis necessary to design the three-dimensional geometry of the flowchannel for suppressing the secondary flow as much as possible, wherebythe formation of secondary vortices, the resulting non-uniform flow, andlarge scale flow separation or the like may be prevented.

SUMMARY OF THE INVENTION

It is therefore an object of the present invention to overcome thedrawbacks of increase of loss and unstable operation of turbomachinerycaused by insufficient suppression of the meridional component ofsecondary flow in the impeller, and to provide the following four designaspects by which the blade profile of the impeller in the turbomachineryis designed using the three-dimensional inverse design method and theimpeller having such blade profile is manufactured to thus reduce theabove loss and improve stability of operation of the turbomachinery.

(1) According to the first aspect of the present invention, there isprovided a turbomachinery having an impeller, characterized in that theimpeller is designed so that the reduced static pressure difference ΔCpor the relative Mach number difference ΔM between the hub and the shroudon the suction surface of a blade shows a remarkable decreasing tendencyalong the location of non-dimensional meridional distance m toward theimpeller exit. Here, non-dimensional meridional distance is defined onthe meridional plane of the impeller as shown in FIG. 1(B). At theshroud, the non-dimensional meridional distance m is defined as m=1_(g)/1_(T).S, which represents the ration of meridional distance 1_(g),measured from the blade inlet 6a along the shroud, to the meridionaldistance 1_(T).S., between the impeller inlet 6a and the impeller exit6b measured along the shroud. Similarly, at the hub, the non-dimensionalmeridional distance m is defined as m=1_(H) /1_(T).H., which representsthe ration of meridional distance 1_(H), measured from the blade inlet6a along the hub, to the meridional distance 1_(T).H., between theimpeller inlet 6a and the impeller exit 6b measured along the hub. So,m-0 corresponds to the impeller inlet 6a, and m=1.0 the impeller exit6b.

With respect to the distribution of the reduced static pressuredifference ΔCp, in order to ensure such remarkable decreasing tendency,as shown in FIGS. 4 and 8, the difference D between a minimum value ΔCpmof reduced static pressure difference ΔCp and a value ΔCp_(m-0).4 ofreduced static pressure difference ΔCp at the location corresponding tonon-dimensional meridional distance mm-0.4 obtained by subtractingnon-dimensional meridional distance 0.4 from non-dimensional meridionaldistance mm representing the above minimum value ΔCpm is selected to benot less than a specified value which is dependent on a specific speedNs of the turbomachinery. In this case, from the viewpoint of secondaryflow suppression in the impeller, the difference D₂₈₀ is preferablyselected to be not less than 0.20 at the specific speed Ns=280, thedifference D₄₀₀ is preferably selected to be not less than 0.28 at thespecific speed Ns=400, and the difference D₅₆₀ is preferably selected tobe not less than 0.35 at the specific speed Ns=560. Further, in order toprevent a flow separation at the location after non-dimensionalmeridional distance mm-0.4 at which the value ΔCp_(m-0).4 of reducedstatic pressure difference ΔCp emerges, the pressure coefficient slopeat the shroud side CPS-s on the suction surface of the blade is selectedto be not less than -1.3 as the lower limit of the pressure coefficientslope at the shroud side CPS-s, _(LIM). Here, the pressure coefficientslope at the shroud side CPS-s on the suction surface of the blade isdefined as a pressure gradient on the shroud surface at the locationbetween the non-dimensional meridional distance mm representing theabove minimum value ΔCpm of reduced static pressure difference ΔCp andthe non-dimensional meridional distance mm-0.4 obtained by subtractingnon-dimensional meridional distance 0.4 from non-dimensional meridionaldistance mm representing the above minimum value ΔCpm. By selectingspecifically this pressure coefficient slope at the shroud side CPS-s onthe suction surface of the blade, the flow separation can be preventedin the downstream side of the location of non-dimensional meridionaldistance mm-0.4. In order to prevent the flow separation in the overallarea of non-dimensional meridional distance m from the impeller inlet tothe impeller exit, especially, in the upstream side of the location ofnon-dimensional meridional distance mm-0.4, the non-dimensionalmeridional distance mm representing the minimum value ΔCpm of reducedstatic pressure difference ΔCp is preferably selected to be in the rangeof non-dimensional meridional distance m=0.8-1.0.

This selection of the location of non-dimensional meridional distance mmrepresenting the minimum value ΔCpm of reduced static pressuredifference ΔCp prevents the gradient of the pressure coefficient curvealong non-dimensional meridional distance m from becoming steep beyond acertain limit at which the flow separation may be generated.

Further, with respect to the distribution of the relative Mach numberdifference ΔM between the hub and the shroud on the suction surface ofthe blade, in order to ensure such remarkable decreasing tendency, asshown in FIGS. 5 and 24, the difference DM between a minimum value ΔMmof relative Mach number difference ΔM and a value ΔM_(m-0).4 of relativeMach number difference ΔM at the location corresponding tonon-dimensional meridional distance mm-0.4 obtained by subtractingnon-dimensional meridional distance 0.4 from non-dimensional meridionaldistance mm representing the above minimum value ΔMm is selected to benot less than a specified value which is dependent on a specific speedNs of the turbomachinery. In this case, the difference DM₄₈₈ is selectedto be not less than 0.23 at the specific speed Ns=488. Further, in orderto prevent a flow separation at the location after non-dimensionalmeridional distance mm-0.4 at which the value ΔM_(m-0).4 of relativeMach number difference ΔM emerges, the Mach number slope at the shroudside MS-s is selected to be not less than -0.8 as the lower limit of theMach number slope at the shroud side MS-s, _(LIM). Here, the Mach numberslope at the shroud side MS-s on the suction surface of the blade isdefined as a gradient of Mach number on the shroud surface at thelocation between the non-dimensional meridional distance mm representingthe above minimum value ΔMm of relative Mach number difference ΔM andthe non-dimensional meridional distance mm-0.4 obtained by subtractingnon-dimensional meridional distance 0.4 from non-dimensional meridionaldistance mm representing the above minimum value.

By selecting specifically this Mach number slope at the shroud side MS-son the suction surface of the blade, the flow separation can beprevented in the downstream side of the location of non-dimensionalmeridional distance mm-0.4. In order to prevent the flow separation inthe overall area of non-dimensional meridional distance m from theimpeller inlet to the impeller exit, especially, in the upstream side ofthe location of non-dimensional meridional distance mm-0.4, thenon-dimensional meridional distance mm representing the minimum valueΔMm of relative Mach number ΔM is preferably selected to be in the rangeon non-dimensional meridional distance m=0.8-1.0.

According to the first aspect of the present invention, while selectingproperly by trial and error the distribution of the meridionalderivative of rV.sub.θ, i.e. blade loading distribution ∂(rV.sub.θ)/∂malong the meridional distance m on the basis of the known closerelationship between the pressure coefficient Cp and the angularmomentum rV.sub.θ, the pressure coefficient Cp is increased ordecreased. And, by utilizing the known three-dimensional inverse designmethod using the blade loading distribution as input data, the impelleris designed so that the above-mentioned characteristic decreasingtendency in the reduced static pressure difference ΔCp or the relativeMach number difference ΔM between the hub and the shroud on the suctionsurface of the blade is realized, and further the above-mentionedcharacteristic limit in the pressure coefficient slope at the shroudside CPS-s or the Mach number slope at the shroud side MS-s on thesuction surface of the blade is realized.

In the turbomachinery having the impeller with the three-dimensionalgeometry obtained by the above design method, the meridional componentof secondary flow can be remarkably suppressed around and after thelocation of non-dimensional meridional distance mm-0.4 where the reducedstatic pressure difference ΔCp or the relative Mach number difference ΔMshows a remarkably decreasing tendency toward the impeller exit. As aresult, the meridional component of secondary flow can be effectivelysuppressed in the overall area of the impeller.

(2) According to the second aspect of the present invention, thedistribution of the reduce static pressure difference ΔCp* alongnon-dimensional meridional distance m on the basis of the pressurecoefficient Cp* which is normalized to clarify dependence on thespecific speed Ns is characterized by a remarkable decreasing tendencytoward the impeller exit.

According to the first aspect of the present invention, since thepressure coefficient Cp or the Mach number M, and thus the reducedstatic pressure difference ΔCp or the relative Mach number difference ΔMare not defined as a function of a specific speed Ns, dependence onnumerical values of them on the specific speed is not quantitativelyclarified. For example, it is difficult to estimate the difference D atthe specific speeds except for the specific speeds illustrated in FIG. 4in the turbomachinery such as pumps which handle incompressible fluid,or the difference DM at the specific speeds illustrated in FIG. 5 in theturbomachinery such as compressors which handle compressible fluid.

Therefore, according to the second aspect of the present invention, inorder to solve the above drawbacks, instead of the pressure coefficientCp or the Mach number M, and thus the reduced static pressure differenceΔCp or the relative Mach number difference ΔM, the normalized pressurecoefficient Cp* is used, whereby the difference D* between a minimumvalue ΔCp*m of the normalized reduced static pressure difference ΔCp*and the normalized reduced static pressure difference ΔCp*_(m-0).4 atthe location corresponding to non-dimensional meridional distance mm-0.4obtained by subtracting non-dimensional meridional distance 0.4 fromnon-dimensional meridional distance mm representing the above minimumvalue ΔCp*m of the normalized reduced static pressure difference ΔCp*can be expressed as a function of the specific speed Ns, as shown inFIG. 6, which is defined by the following equation:

    D*=-0.004Ns+3.62

Therefore, in order to suppress the secondary flow in the impeller, forexample, the difference D₅₀₀ is preferably selected to be not less than1.62 at the specific speed Ns=500, the difference D₄₀₀ is preferablyselected to be not less than 2.02 at the specific speed Ns=400, and thedifference D₃₀₀ is preferably selected to be not less than 2.42 at thespecific speed Ns=300.

Here, the normalized pressure coefficient Cp* is defined as follows:

Cp*=Cp/Cp, mid-mid

where Cp, mid-mid is a pressure coefficient in the center of flowchannel (midspan and midpitch) at the location of non-dimensionalmeridional distance as shown in FIG. 1(D). Incidentally, the pressurecoefficient Cp* in compressible fluid which is handled by theturbomachinery such as a compressor is expressed by the followingequation.

    Cp*=2[1-(1-0.5W.sup.2 /H.sub.0 *).sup.γ/(γ-1) ]/γM.sub.0.sup.*2

    M.sub.0.sup.*2 =Ut/(γP.sub.0 */ρ.sub.0 *).sup.0.5

where Ut is a peripheral speed of the impeller, W is a relativevelocity, H₀ * is a rothalpy, γ is a ratio of specific heat, P₀ * isrotary stagnation pressure, and ρ₀ * is a density corresponding to P₀ *.

According to the second aspect of the present invention, it is possibleto select a wide range of specific speeds Ns in the turbomachinery anddeal with every kind of fluid (compressible fluid and incompressiblefluid) which is handled by the turbomachinery, and while selectingproperly by trial and error the blade loading distribution alongnon-dimensional meridional distance m on the basis of the known closerelationship between the pressure coefficient Cp and the angularmomentum rV_(s), the pressure coefficient Cp* is increased or decreased.And, by utilizing the known three-dimensional inverse design methodusing the blade loading distribution as input data, the impeller isdesigned so that the above-mentioned characteristic deceasing tendencyin the reduced static pressure difference ΔCp* between the hub and theshroud on the suction surface of the blade is realized.

In the turbomachinery having the impeller with the three-dimensionalgeometry obtained by the above design method, the meridional componentof secondary flow can be remarkably suppressed after the location ofnon-dimensional meridional distance mm-0.4 where the normalized reducedstatic pressure difference ΔCp* shows a remarkably decreasing tendencytoward the impeller exit. As a result, the meridional component ofsecondary flow can be effectively suppressed in the overall area of theimpeller.

(3) According to the third aspect of the present invention, there isprovided a method of designing and manufacturing the turbomachineryhaving the impeller with the three-dimensional geometry which realizesthe distribution of the reduced static pressure difference ΔCp or therelative Mach number difference ΔM along non-dimensional distance m andis characterized by the first aspect of the present invention.

According to the fourth aspect of the present invention, there isprovided a method of designing and manufacturing the turbomachineryhaving the impeller with the three-dimensional geometry which realizesthe distribution of the reduced static pressure difference ΔCp* on thebasis of the normalized pressure coefficient Cp* along non-dimensionaldistance m and is characterized by the second aspect of the presentinvention.

According to the third and fourth aspects of the present invention,while selecting properly by trial and error the blade loadingdistribution along non-dimensional meridional distance m on the basis ofthe known close relationship between the pressure coefficient Cp and theangular momentum rV_(s), the pressure coefficient Cp is increased ordecreased, and by utilizing the known three-dimensional inverse designmethod using the blade loading distribution as input data, thethree-dimensional geometry of the impeller which realizes thedistribution characterizing the first and second aspects of the presentinvention is established.

In this case, the design method of the three-dimensional geometry of theimpeller is processed in accordance with a flow chart in FIG. 3(B).

In the first step (step of determining meridional surface), the designspecification is input to determine the meridional geometry of theimpeller and the number of blades of the impeller. Next, a plurality ofsurfaces of revolution is defined in a meridional flow channel, andstacking condition f₀ representing tangential co-ordinate of bladecamber line at a point on each of surfaces of revolution is determined.

In the second step (step of determining the specified loadingdistribution), the profile of the blade loading distribution∂(rV_(s))/∂m is selected so that the blade loading distribution has apeak on the shroud surface in the first half of the location ofnon-dimensional meridional distance m and a peak on the hub surface inthe latter half of the location of non-dimensional meridional distancem. Next, the value obtained by integration of the blade loadingdistribution along the non-dimensional distance m is adjusted to satisfydesign head of the impeller, the distribution of blade loading rV_(s)along the location of non-dimensional meridional distance m isdetermined.

In the third step (step of determining blade profile), the blade shapeis computed in an iterative manner by integrating

    {(Vz+v.sub.zb1)∂f/∂z}+}(Vr+v.sub.rb1).differential.f/∂r}={(rV.sub.s)/r.sup.2)}+{(v.sub.ab1)/r}-ω

along non-dimensional meridional distance m using stacking conditionf_(o) determined by the first step as an initial value. In the firstiteration the equation is integrated by neglecting the periodic velocityterms (v_(rb1), v_(zb1), v_(sb1)) and using the approximate value for Vrand Vz and using V_(s) from the specified rV_(s) distribution.Integrating this equation the tangential co-ordinate of the blade camberline f along the non-dimensional meridional distance m is determined.The three-dimensional geometry of the impeller is then determined byadding a certain thickness to the determined blade camber line to allowthe blade to have a required mechanical strength. The flow field in theblade channel is then calculated by solving the governing equation ofthe mean and tangentially periodic flow fields. The solution of the meanflow field governing equation then gives new values for Vr and Vz, whilefrom the solution of the periodic flow governing equation the velocityterms v_(rb1), v_(zb1) and v_(sb1) are determined. Using these updatedvalues the above equation is again integrated to find the new tangentialco-ordinate of the blade camber line f along the non-dimensionalmeridional distance m. This process is repeated until the difference inblade camber line between one iteration and the next falls below acertain tolerance.

In the fourth step (step of evaluation of optimum reduced staticpressure difference and the like), it is judged whether or not thedistribution of the reduced static pressure difference ΔCp or therelative Mach number difference ΔM along non-dimensional meridionaldistance m which is computed in the third step is suitable forsuppressing the secondary flow in the impeller.

In the fifth step (step of evaluating flow fields), a possibility ofpoor performance caused by a flow separation due to rapid decelerationof flow in the impeller determined by the third step is evaluated. Next,it is evaluated whether the secondary flow parameter is a satisfiedvalue or not. In the case where it is judged that the pressuredistribution in the impeller is not appropriate, after going back to thesecond step to modify the blade loading distribution, the steps from thesecond step to the fifth step are repeated until the expected result isachieved.

According to the method of manufacturing the turbomachinery of the thirdand fourth aspects, the blade loading distribution, which is directlyrelated to characteristics of flow fields of D, DM or D* which iscriteria of judgement in the fourth process, is determined and is usedas input data for the third step for determining blade profile.Therefore an effective blade profile for suppressing secondary flow ispromptly obtained, compared with the conventional manufacturing methodusing the blade angle distribution as a parameter related to the bladeprofile.

BRIEF DESCRIPTION OF DRAWINGS

FIGS. 1(A)-2(B) are views for explaining the background art;

FIGS. 1(A) through 1(E) are views for explaining the meridionalcomponent of secondary flow in three-dimensional geometry of a closedtype impeller, FIG. 1(A) is a perspective view partly in section, FIG.1(B) is a meridional cross-sectional view taken along line A-A' of FIG.1(A), FIG. 1(C) is a view for explaining a computational mesh inthree-dimensional viscous calculations, FIG. 1(D) is a perspective viewshowing midspan and midpitch of the impeller, and FIG. 1(E) is a viewshowing a blade profile of the impeller;

FIGS. 2(A) and 2(B) are views for explaining secondary vortices causedby the meridional component of secondary flow in the closed typeimpeller, FIG. 2(A) is a perspective view partly in section, and FIG.2(B) is a cross-sectional view taken along line B-B' of FIG. 2(A);

FIGS. 3(A) and 3(B) are flow charts of numerical analysis by a computerto determine a three-dimensional shape of the impeller in theturbomachinery,

FIG. 3(A) is a flow chart showing a conventional design method ofdesigning the three-dimensional geometry of the impeller, and

FIG. 3(B) is a flow chart showing a three-dimensional inverse designmethod which has been put to practical use recently, according to thepresent invention;

FIG. 4 is a graph showing verification data plotted on the plane definedby a vertical axis representing the pressure coefficient slope at theshroud side CPS-s and a horizontal axis representing the pressurecoefficient slope at the hub side CPS-h, and further showing boundarylines defined by specific speeds Ns and the lower limit of the pressurecoefficient slope at the shroud side CPS-s,_(LIM) ;

FIG. 5 is a graph showing verification data plotted on the plane definedby a vertical axis representing the Mach number slope at the shroud sideMS-s and a horizontal axis representing the Mach number slope at the hubside MS-h, and further showing boundary lines defined by specific speedsNs and the lower limit of the Mach number slope at the shroud sideMS-s,_(LIM) ;

FIG. 6 is a graph showing verification data plotted on the plane definedby a vertical axis representing the difference D* between a minimumvalue ΔCp*m of the normalized reduced static pressure difference ΔCp*and a value ΔCp*_(m-0).4 of the normalized reduced static pressuredifference ΔCp* at the location corresponding to non-dimensionalmeridional distance mm-0.4 obtained by subtracting non-dimensionalmeridional distance 0.4 from non-dimensional meridional distance mmrepresenting the above minimum value ΔCp*m and a horizontal axisrepresenting a specific speed Ns, and further showing boundary linesdefined by specific speeds Ns, thereby expressing the above differenceD* as a function of the specific speeds Ns;

FIG. 7(A) is a table showing the pressure coefficient slope at theshroud side CPS-s and the pressure coefficient slope at the hub sideCPS-h read from characteristic graphs in verification examples, andMSF-angle calculated as secondary flow parameter, and

FIG. 7(B) is a table showing the difference D* on the basis of thenormalized pressure coefficient Cp* shown in the same manner as FIG.7(A);

FIGS. 8 through 22 are characteristic graphs showing the distribution ofthe pressure coefficient Cp along non-dimensional meridional distance mof the blade, FIG. 8 is a graph showing a verification example "A",

FIG. 9 is a graph showing a verification example "B",

FIG. 10 is a graph showing a verification example "C",

FIG. 11 is a graph showing a verification example "D",

FIG. 12 is a graph showing a verification example "E",

FIG. 13 is a graph showing a verification example "F",

FIG. 14 is a graph showing a verification example "G",

FIG. 15 is a graph showing a verification example "H",

FIG. 16 is a graph showing a verification example "I",

FIG. 17 is a graph showing a verification example "J",

FIG. 18 is a graph showing a verification example "K",

FIG. 19 is a graph showing a verification example "L",

FIG. 20 is a graph showing a verification example "M",

FIG. 21 is a graph showing a verification example "N", and

FIG. 22 is a graph showing a verification example "O";

FIG. 23 is a flow vector diagram showing the state of flow separation inthe verification example "O";

FIG. 24 through FIG. 29 are characteristic graphs showing thedistribution of the Mach number along non-dimensional meridionaldistance m of the blade,

FIG. 24 is a graph showing a verification example "P",

FIG. 25 is a graph showing a verification example "Q",

FIG. 26 is a graph showing a verification example "R",

FIG. 27 is a graph showing a verification example "S",

FIG. 28 is a graph showing a verification example "T", and

FIG. 29 is a graph showing a verification example "U";

FIG. 30 is a flow vector diagram showing the state of flow separation inthe verification example "U".

BEST MODE FOR CARRYING OUT THE INVENTION

An embodiment according to the first aspect of the present inventionwill be described below.

The influence of viscosity can be neglected for main flow of therelative flow in the flow channels of an impeller, therefore thefollowing formula is approximately satisfied in incompressible flow asin a liquid pump.

    P.sub.0 *=p*+0.5ρW.sup.2 =constant

where P₀ * is rotary stagnation pressure upstream of the impeller.

Next, as a non-dimensional quantity of reduced static pressure p* on theblade surface, pressure coefficient Cp is defined by the followingequation:

    Cp=(P.sub.0 *-p*)/(0.5ρUt.sup.2)=(W/Ut).sup.2

where Ut represents the mean peripheral speed at the impeller exit.

As is apparent from the above equation, the pressure coefficient Cp islarge at the shroud where reduced static pressure p* is low, and issmall at the hub where reduced static pressure p* is high. As mentionedabove, since the meridional component of secondary flow on the bladesuction surface is directed to the shroud side having low reduced staticpressure p* from the hub side having high reduced static pressure p*,suppression of the meridional component of secondary flow can beexpected by reducing pressure difference ΔCp between them. Incidentally,in case of incompressible fluid, the pressure coefficient Cp is equal to(W/Ut)², where W is relative velocity. In compressible fluid as in acompressor, the physical variable related to the behavior of secondaryflow is relatively Mach number. In order to simplify the description,only the distribution of the pressure coefficient Cp will be describedbelow. The influence of distribution of the pressure coefficient Cp inincompressible flow upon the meridional component of secondary flow isequivalent to that of the relative Mach number M in compressible flow.Here, static pressure p or relative Mach number M is obtained throughthree-dimensional steady inviscid flow calculation.

Since the boundary layers on the blade surfaces which develop along thewall of the flow channel in the impeller increase their thicknesscumulatively from the impeller inlet toward the impeller exit, thepresent invention proposes structure for suppressing the meridionalcomponent of secondary flow on the suction surface of the blade,considering distribution of the pressure coefficient Cp mainly in thelatter half of the impeller. That is, the blade profile is designed soas to have the pressure distribution so that the pressure difference ΔCpbetween the shroud side and the hub side on the suction surface shows aremarkably decreasing tendency along the location of non-dimensionalmeridional distance m toward the impeller exit.

FIG. 8 is a characteristic graph showing distribution of the pressurecoefficient Cp obtained by the three-dimensional steady inviscid flowcalculations, and thus the reduced static pressure difference ΔCp of apump according to a best mode of the first aspect of the presentinvention. In FIG. 8, the vertical axis represents the pressurecoefficient Cp, and the horizontal axis represents the location betweennon-dimensional meridional distance m=0 (impeller inlet) andnon-dimensional meridional distance m=1.0 (impeller exit). In FIG. 8, asolid curve at the upper part of the graph shows a pressure coefficientcurve representing values of the pressure coefficient on the suctionsurface of the blade at the shroud side along the location ofnon-dimensional meridional distance m, and an alternative long and shortdash curve extending substantially along the above solid line showsvalues of the pressure coefficient at the midpitch location on theshroud surface.

On the other hand, in FIG. 8, a solid curve at the lower part of thegraph shows a pressure coefficient curve representing values of thepressure coefficient on the suction surface of the blade at the hub sidealong the location of non-dimensional meridional distance m, and analternative long and short dash curve extending substantially along theabove solid line shows values of the pressure coefficient at themidpitch location on the hub surface.

Broken line curves show the pressure coefficient on the pressure surfaceof the blade at the shroud and hub sides, respectively. These curves arenot directly related to the present invention, but are depicted forreference.

In FIG. 8, the distance between the solid curves adjacent to each otheralong the vertical axis, i.e. the difference between a value on thepressure coefficient curve at the shroud side and a value on thepressure coefficient curve at the hub side at the same location ofnon-dimensional meridional distance m corresponds to the reduced staticpressure difference ΔCp. The location of non-dimensional meridionaldistance mm at which a minimum value ΔCpm (in case of a negative value,a maximum value of absolute value) of reduced static pressure differenceΔCp emerges is defined on the horizontal axis, and the location whichapproaches the impeller inlet (m=0) by non-dimensional meridionaldistance 0.4 from the location of non-dimensional meridional distancemm, that is: the location corresponding to non-dimensional meridionaldistance mm-0.4 obtained by subtracting non-dimensional meridionaldistance 0.4 from non-dimensional meridional distance mm representingthe above minimum value ΔCpm is defined.

Here, the gradient of inclined straight line which connects the valueC_(s).m-0.4 on the pressure coefficient curve on the shroud surface atthe location of non-dimensional meridional distance mm-0.4 and the valueCp_(s).m on the pressure coefficient curve on the shroud surface at thelocation of non-dimensional meridional distance mm, i.e. (Cp_(s).m-Cp_(s).m-0.4)/0.4 is defined as a pressure coefficient slope at theshroud side CPS-s. In the example of FIG. 8, the pressure coefficientslope at the shroud side CPS-s is negative. Similarly, the gradient ofstraight line which connects the value Cp_(h).m-0.4 on the pressurecoefficient curve on the hub surface at the location of non-dimensionalmeridional distance mm-0.4 and the value Cp_(h).m on the pressurecoefficient curve on the hub surface at the location of non-dimensionalmeridional distance mm, i.e. (Cp_(h).m -Cp_(h).m-0.4)/0.4 is defined aspressure coefficient gradient at the hub side CPS-h. In the example ofFIG. 8, the pressure coefficient slope at the hub side CPS-h ispositive.

It was confirmed on the basis of many verification examples by theinventors of the present invention that the difference between the valueon the pressure coefficient curve at the shroud side at the location ofnon-dimensional meridional distance mm-0.4 and the value on the pressurecoefficient curve at the hub side at the location of non-dimensionalmeridional distance mm-0.4, that is, the difference D between thereduced static pressure difference ΔCp_(m-0).4 at the location ofnon-dimensional distance mm-0.4 and the minimum value ΔCpm of thereduced static pressure difference ΔCp is the essential factor whichgoverns suppression of the secondary flow in the impeller of theturbomachinery. Here, the difference D is derived from cooperativecontribution of the pressure coefficient slope at the shroud side CPS-sand the pressure coefficient slope at the hub side CPS-h, thus thedifferences D between the reduced static pressure difference ΔCp_(m-0).4at the location of non-dimensional meridional distance mm-0.4 and theminimum value ΔCpm of the reduced static pressure difference ΔCp inprincipal verification examples were plotted in FIG. 4 on the planedefined by horizontal and vertical axes representing the aboverespective slopes or gradients. In FIG. 4, the vertical axis representsthe pressure coefficient slope at the shroud side CPS-s, and thehorizontal axis represents the pressure coefficient slope at the hubside CPS-h. In FIG. 4, Δ represent verification examples of pumps of aspecific speed Ns=280, □ represent verification examples of pumps of aspecific speed Ns=400, and  represent verification examples of pumps ofa specific speed Ns=560. Further, open symbols (Δ, □, ) representadaptation to the quantitative criterion (describe latter) of judgementabout suppression of the secondary flow, and solid symbols (▴, ▪, )represent nonadaptation to the above criterion.

FIG. 7(A) is a table showing data in principal verification examples.FIG. 7(A) includes six verification examples A, B, C, D, 1 and 2 inpumps of a specific speed Ns=280. Concerning four examples A, B, C andD, four pairs of data as to values of the pressure coefficient slope atthe shroud side CPS-s and the pressure coefficient slope at the hub sideCPS-h were read from the pressure coefficient curves of the verificationexamples shown in FIGS. 8 through 11 in the order of A, B, C and D, andfour Δ symbols were plotted on the plane between two axes from thereadings. Concerning two examples 1 and 2, the pressure coefficientcurves in the verification examples are not shown, but the resultantdata were represented for reference as a part of large amount of otherverification examples.

Four verification examples A, B, C and D in pumps of a specific speedNs=400 are the same as the above. Four pairs of data as to values of thepressure coefficient slope at the shroud side CPS-s and the pressurecoefficient slope at the hub side CPS-h were read from the pressurecoefficient curves of the verification examples shown in FIGS. 12through 15 in the order of E, F, G and H, and four □ symbols wereplotted in FIG. 4. Further, six verification examples I, J, K, L, M andN in pumps of a specific speed Ns=560 are the same as the above. Dataconcerning values of the pressure coefficient slope at the shroud sideCPS-s and the pressure coefficient slope at the hub side CPS-h were readfrom the pressure coefficient curves of the verification examples shownin FIGS. 16 through 21 in the order of I, J, K, L, M and N, and six Osymbols were plotted in FIG. 4. Concerning verification examples 3, 4,5, 6 and O, the resultant data were represented for reference.

In the plotted data in FIG. 4, as described above, open and solidsymbols represent adaptation or nonadaptation to the quantitativecriterion of judgement about suppression of the secondary flow. Thequantitative criterion of judgement will be described below.

FIG. 1(C) is an explanatory view used for the three-dimensional viscousflow calculation and showing the relationship between the computationalmeshes inside the bladed region and the secondary flow angle α definedin each of the computational meshes. Since the secondary flow is definedas flow which has a velocity component deviating from the direction ofthe computational mesh, the computational mesh to be used as a basis isrequired to have a certain regularity. That is, mesh is dividedregularly (i.e. mesh division is applied at the same number of meshpoints and the same ratio of mesh spacing) between the blade leadingedge and the blade trailing edge in J direction on the hub and theshroud surfaces, and meshes of the spanwise direction (K direction) ineach J location which connects two corresponding points on the hubsurface and the shroud surface are divided regularly, whereby thecomputational mesh is defined over the entire bladed region. Suchcomputational mesh is generally used in three-dimensional viscouscalculations.

MSF-angle used as the quantitative criterion of judgement aboutsuppression of the secondary flow is expressed by the followingequation. ##EQU1## where α is an angle between the tangential directionalong the streamwise mesh (J direction) and the direction of themeridional velocity vector at the location near the suction surface ofthe blade in each computational mesh in the blade region in FIG. 1(C);

V_(m) is meridional velocity;

s is the non-dimensional meridional span length in K direction, s being0 on the hub surface and 1 on the shroud surface on each JthQuasi-orthogonal line (mesh line of K direction);

m is the non-dimensional meridional distance in J direction, m being 0at the blade leading edge and 1 at the blade trailing edge on each Kthstream surface;

[ ]_(ss) is integrated value in the first mesh from the suction surfaceof the blade.

That is, MSF-angle is defined as mass-averaged value of the magnitude ofthe flow deviation angle from the streamwise mesh direction over theentire suction surface of the blade.

There is a tendency that when flow which has impinged on the blade atthe impeller inlet portion moves around the blade leading edge, a partof flow deviates from the mesh direction. Since this deviation angle hasno meaning in the secondary flow caused by viscous action in theboundary layer on the blade surface, in order to eliminate the influenceof the above deviating flow, integration is made excluding the regionbetween non-dimensional meridional distance m=0.0 and m=0.15 in whichthe boundary layer is thin.

In FIG. 7(A), the values of MSF-angle which were calculated by the aboveequation, the pressure coefficient slope at the shround side CPS-s andthe pressure coefficient slope at the hub side CPS-h in verificationexamples are shown.

On the other hand, the values of MSF-angle in a large amount ofverification examples have been calculated by the same manner, and therelationship between the values of MSF-angle calculated in theverification examples and lowering of performance caused by thesecondary flow in the verification examples has been studied by theinventors of the present invention. As a result, it was confirmed thatas the quantitative criterion of judgement about the suppression of thesecondary flow, the selection of the following MSF-angle is appropriatefor each of the groups having similar numbers of mesh points and thespecific speed.

MSF-angle as the criterion of judgement is 18 degrees in the pump of thespecific speed Ns=280.

MSF-angle as the criterion of judgement is 15 degrees in the pump of thespecific speed Ns=400.

MSF-angle as the criterion of judgement is 25 degrees in the pump of thespecific speed Ns=560.

MSF-angle as the criterion of judgment is 15 degrees in the compressorof the specific speed Ns=488.

By comparing the values of MSF-angle shown in FIG. 7(A) representing themagnitude of secondary flow which is expressed quantitatively in each ofverification examples with the confirmed value of MSF-angle for each ofthe groups as the quantitative criterion of judgment about the action ofthe secondary flow suppression, the value of MSF-angle in eachverification example equal to or larger than the value of MSF-angle asthe criterion of judgment means nonadaptation to the above criterion ofjudgement (insufficient action of secondary flow suppression), and thevalue of MSF-angle in each verification example smaller than the valueof MSF-angle as the criterion of judgment means adaptation to the abovecriterion of judgment (sufficient action of secondary flow suppression).The data of nonadaptation are shown by solid symbols, and the data ofadaptation are shown by open symbols in FIG. 4.

As shown in FIG. 4, a boundary line between data area of solid symbolswhich show nonadaptation to the criterion and data area of open symbolswhich show adaptation to the criterion can be drawn on the basis of dataplotted in FIG. 4 for each of specific speeds Ns. In the drawing, thethree positively sloped straight lines are boundary lines whichcorrespond to the specific speeds Ns=280, Ns=400, and Ns=560,respectively. In each of the specific speeds Ns, the data area locatedat the lower right side of the boundary line corresponds to the dataarea of adaptation to the criterion. By further examination of theboundary line, each of data on the boundary line is such that thedifference between values of the pressure coefficient slope at theshroud side CPS-s positioned along the vertical axis and values of thepressure coefficient slope at the hub side CPS-h positioned along thehorizontal axis is maintained at a constant value. That is, the boundaryline concerning the specific speed Ns=280 corresponds to the inclinedstraight line representing (the value of the pressure coefficient slopeat the hub side CPS-h)-(the value of the pressure coefficient slope atthe shroud side CPS-s)=0.2/0.4=0.5. Therefore, as shown in FIG. 8, thismeans that the difference D₂₈₀ between a minimum value .increment.Cpm ofthe reduced static pressure difference .increment.Cp and a value.increment.Cpm-0.4 of the reduced static pressure difference.increment.Cp at the location corresponding to non-dimensionalmeridional distance mm-0.4 obtained by subtracting non-dimensionalmeridional distance 0.4 from non-dimensional meridional distance mmrepresenting the minimum value .increment.Cpm is maintained to be 0.20.Therefore, concerning data of the specific speed Ns=280, the data inwhich the difference D₂₈₀ is not less than 0.2 are plotted by opensymbols in the data area of adaptation to the criterion located at thelower right side of the boundary line concerning the specific speedNs=280. Thus, the impeller in which the difference D₂₈₀ is not less than0.2 is suitable for suppression of the secondary flow.

The boundary line concerning the specific speed Ns=400 corresponds tothe inclined straight line representing (the value of the pressurecoefficient slope at the hub side CPS-h)--(the value of the pressurecoefficient slope at the shroud side CPS-s)=0.28/0.4=0.7. It can be saidthat this case is the same tendency as that of the specific speedNs=280. Therefore, the impeller in which the difference D₄₀₀ is not lessthan 0.28 is suitable for suppression of the secondary flow.

Further, the boundary line concerning the specific speed Ns=560corresponds to the inclined straight line representing (the value of thepressure coefficient slope at the hub side CPS-h)-(the value of thepressure coefficient slope at the shroud side CPS-s)=0.35/0.4=0.87. Itcan be said that this case is also the same tendency as of the specificspeed Ns=280. Therefore, the impeller in which the difference D₅₆₀ isnot less than 0.35 is suitable for suppression of the secondary flow.

As is apparent from the above description, data area of open symbolswhich are suitable for suppression of the secondary flow on the planebetween the pressure coefficient slope at the shroud side CPS-s and thepressure coefficient slope at the hub side CPS-h means that thedifference D between .increment.Cpm-0.4 at the location ofnon-dimensional meridional distance mm-0.4 and the minimum value.increment.Cpm of the reduced static pressure difference .increment.Cpat the location of non-dimensional meridional distance mm can not beless than a certain value which is dependent on the criterion ofjudgment about suppression of the secondary flow. The value of thedifference D is the result of cooperative contribution of the value ofthe pressure coefficient slope at the shroud side CPS-s on the verticalaxis on the boundary line and the value of the pressure coefficientslope at the hub side CPS-h on the horizontal axis. The degree ofcontribution of both slopes varies in a wide range; there are threecases, i.e. the first case (1) which is largely dependent on thedecreasing tendency of the pressure coefficient slope at the shroudside, the second case (2) which is dependent on the increasing tendencyof the pressure coefficient slope at the hub side, and the third case(3) which is dependent on moderate harmonization of the decreasingtendency and the increasing tendency of both slopes. However, it wasconfirmed by the inventors of the present invention that as shown inFIG. 8, there exists a lower limit of the pressure coefficient slope atthe shroud side CPS-s,_(LIM) having a lower limit of negative value inthe aft part from the location of non-dimensional meridional distancemm-0.4 to the impeller exit (m=1.0), and in the case where the formationof the difference D is dependent largely on the value of the pressurecoefficient slope at the shroud side CPS-s less than the lower limit ofthe pressure coefficient slope at the shroud side CPS-s,_(LIM), the flowseparation occurs in the aft part from the location of non-dimensionalmeridional distance mm-0.4 to the impeller exit (m=1.0), generatingsignificant reduction in head and efficiency.

The lower limit of the pressure coefficient slope at the shroud sideCPS-s,_(LIM) thus confirmed is -1.3, and this is proved by the fact thatthe horizontal straight line, which defines data area generating flowseparation and including three verification examples 5, 6, and O at thelower side of the line, can be drawn. As an example, FIG. 23 is a flowvector diagram showing the state of flow separation in the verificationexample of O.

It was confirmed by the inventors of the present invention that the flowseparation emerges in the aft part from the location of non-dimensionalmeridional distance mm-0.4 to the impeller exit (m=1.0) when CPS-s isless than the lower limit of CPS-s,_(LIM), but there exists anotherlower limit in the fore part of the blade toward the impeller inlet(m=0) difference from the lower limit of the pressure coefficient slopeat the shroud side CPS-s,_(LIM) in the aft part from the location ofnon-dimensional meridional distance mm-0.4. In order to prevent flowseparation caused by the steep pressure coefficient slope at the shroudside in the fore part of the location toward the impeller inlet (m=0),the location of non-dimensional meridional distance mm at which theminimum value .increment.Cpm of the reduced static pressure difference.increment.Cp emerges is preferably selected to be in the range ofnon-dimensional meridional distance m=0.8-1.0, i.e. in the aft parttoward the impeller exit (m=1.0).

Further, in the lower part of FIG. 7(A), concerning compressor of aspecific speed Ns=488, the values of Mach number slope at the shroudside MS-s, the values of Mach number slope at the hub side MS-h and thevalues of MSF-angle are shown for eight examples of P, 9, Q, R, S, T, Uand 10. The data of verification examples were plotted on the plane ofFIG. 5 corresponding to that of FIG. 4 in the same manner as FIG. 4.

As described above, in compressors which handle compressible fluid, itis known that the pressure coefficient slope at the shroud side CPS-sand the pressure coefficient slope at the hub side CPS-h correspond tothe Mach number slope at the shroud side MS-s and the Mach number slopeat the hub side MS-h, respectively. The plane in FIG. 5 is defined by avertical axis representing the Mach number slope at the shroud side MS-sand a horizontal line representing the Mach number slope at the hub sideMS-h.

From a large amount of verification data including principalverification examples plotted on the plane of FIG. 5, as a boundary lineconcerning a compressor of a specific speed Ns=488, an inclined straightline representing (the value of the Mach number slope at the hub sideMS-h)-(the value of the Mach number slope at the shroud sideMS-s)=(0.23/0.4)=0.575 can be drawn, and data area located at the lowerright side of the boundary line corresponds to data area of adaptationto the criterion of judgment about suppression of the secondary flow.

This means that in the compressor of a specific speed Ns=488, thedifference MD₄₈₈ between a minimum value .increment.Mm of the reducedstatic pressure difference .increment.M and a value .increment.Mm-0.4 ofthe reduced static pressure difference .increment.M at the locationcorresponding to non-dimensional meridional distance mm-0.4 obtained bysubtracting non-dimensional meridional distance 0.4 from non-dimensionalmeridional distance mm representing the minimum value .increment.Mm ismaintained to be 0.23. Therefore, it was confirmed from a large amountof verification examples that the impeller in which the difference MD₄₈₈is not less than 0.23 and which corresponds to data area shown by opensymbols is suitable for suppression of the secondary flow.

However, it was confirmed by the inventors of the present invention thatthere exists a lower limit of the Mach number slope at the shroud sideMS-s,_(LIM) and in the case where the value of the Mach number slope atthe shroud side MS-s is less than the lower limit of the Mach numberslope at the shroud side MS-s,_(LIM), the flow separation is generatedin the aft part from the location of non-dimensional meridional distancemm-0.4 to the impeller exit (m=1.0), generating significant reduction inhead and efficiency.

The lower limit of the pressure coefficient slope at the shroud sideCPS-s,_(LIM) thus confirmed is -0.8 in the compressor of the specificspeed Ns=488, and this is proved by the fact that the horizontalstraight line, which defines data area generating flow separation andincluding two verification examples, U and 10 at the lower side of theline, can be drawn. As an example, FIG. 30 is a flow vector diagramshowing the state of flow separation in the verification example of U.

It was confirmed by the inventors of the present invention that the flowseparation emerges in the aft part from the location of non-dimensionalmeridional distance mm-0.4 to the impeller exit (m=1.0) when MS-s islower than the lower limit of MS-s,_(LIM), but there exists anotherlower limit in the fore part of the blade toward the impeller inlet(m=0) difference from the lower limit of the Mach number slope at theshroud side MS-s,_(LIM) in the aft part from the location ofnon-dimensional meridional distance mm-0.4. In order to present flowseparation caused by the steep Mach number slope at the shroud side inthe fore part of the location toward the impeller inlet (m=0), thelocation of non-dimensional meridional distance mm at which the minimumvalue .increment.Cpm of the reduced static pressure difference.increment.Cp emerges is preferably selected to be in the range ofnon-dimensional meridional distance m=0.8-1.0, i.e. in the aft parttoward the impeller exit (m=1.0).

Referring back to FIG. 7(A), in the lower part of FIG. 7(A), concerningcompressor of a specific speed Ns=488, values of the Mach number slopeat the shroud side MS-s and the Mach number slope at the hub side MS-h,as can be referenced in FIG. 25, were read from the Mach number curvesof the verification examples shown in FIGS. 24 through 29 in the orderof P, Q, R, S, T and U, and shown. In each of the verification examples,the calculation process of MSF-angle, the criterion of judgment byMSF-angle and the evaluation process for evaluating the secondary flowsuppression quantitatively are the same as the description related toFIG. 4, thus further explanation may be omitted.

In the present invention, the verification examples in FIG. 4 for pumpsare presented in the range of the specific speed Ns=280-560. Accordingto the concept of the present invention, there will be another optimumvalue for the range of the specific speed of not more than Ns=280.However, as is observed from the tendency of the inclined boundary linesin FIG. 4, the D₂₈₀ value is lower than D₄₀₀ and D₅₆₀ value, and D₄₀₀value is lower than D₅₆₀ value. So, the critical value of D has atendency to have a lower value for an impeller having a lower specificspeed, although the quantitative dependency on the specific speed is notclear in FIG. 4 (the quantitative dependency is clarified in thefollowing second aspect of the present invention). Therefore, theimpeller, having suppressed meridional secondary flow, can be designedin safety by using D value of not less than D₂₈₀ =0.2 for the specificspeed range of not more than Ns=280. Similarly, the impellers, havingsuppressed meridional secondary flows, for the specific speed range ofnot more than Ns=400 and Ns=560 can be designed in safety by using Dvalue of not less than D₄₀₀ =0.28 and D₅₆₀ =0.35, respectively.

In the compressor, only the data of the specific speed of Ns=488 arepresented in FIG. 5. However, the flow mechanism leading to thesuppression of the meridional secondary flows is the same between pumpsand compressors, and so that compressor impellers, having suppressedmeridional secondary flow, for the specific speed range of not more thanNs=488 can be designed in safety by using DM value of not less thanDM₄₈₈ =0.23.

Next, an embodiment according to the second aspect of the presentinvention will be described below.

According to the embodiment of the first aspect of the presentinvention, the boundary lines of the inclined straight lines areconfirmed and drawn in FIG. 4 or FIG. 5 dispersively for each of thespecific speeds of the turbomachinery or sorts of fluid (incompressiblefluid or compressible fluid), and the dependence of data on the specificspeed is not made evident quantitatively. Therefore, concerning theturbomachinery having a certain specific speed and handling a certainkind of fluid, when designing suitably the contribution in the pressurecoefficient slope at the shroud side CPS-s and the pressure coefficientslope at the hub side CPS-h or the Mach number slope at the shroud sideMS-s and the Mach number slope at the hub side MS-h from the aspect ofsecondary flow suppression so that the difference D between a minimumvalue .increment.Cpm of the reduced static pressure difference.increment.Cp and the value .increment.Cpm-0.4 of the reduced staticpressure difference .increment.Cp at the location corresponding tonon-dimensional meridional distance mm-0.4 obtained by subtractingnon-dimensional meridional distance 0.4 from non-dimensional meridionaldistance mm representing the minimum value .increment.Cpm or thedifference DM between the minimum value .increment.Mm of the relativeMach number difference .increment.M and a value .increment.Mm-0.4 of therelative Mach number difference .increment.M at the locationcorresponding to non-dimensional meridional distance obtained bysubtracting non-dimensional meridional distance 0.4 from non-dimensionalmeridional distance representing the minimum value amounts to a certainvalue or more, there are cases to which the boundary lines shown on theplane of FIG. 4 or FIG. 5 are not directly applicable.

Therefore, according to the second aspect of the present invention, withrespect to the difference D between a minimum value .increment.Cpm ofthe reduced static pressure difference .increment.Cp and a value.increment.Cpm-0.4 of the reduced static pressure difference.increment.Cp or the difference DM between a minimum value .increment.Mmof the relative Mach number difference .increment.M and a value.increment.Mm-0.4 of the relative Mach number difference .increment.M,the dependence on the specific speed is clarified in spite of the typesof fluid. That is, concerning the difference D or DM, the pressurecoefficient Cp* which is normalized by the pressure coefficient Cp,mid-mid in the center of fluid passage is introduced and newly defined,whereby the boundary line according to the first aspect of the presentinvention can be expressed as a function of the specific speed Ns.

FIG. 6 shows the plotted data about the above difference on the basis ofthe normalized pressure difference Cp* in verification examples. In FIG.6, the vertical axis represents the difference D* between the normalizedreduced static pressure difference .increment.Cp*m-0.4 at the locationof non-dimensional meridional distance mm-0.4 and a minimum value.increment.Cp*m the normalized reduced static pressure difference.increment.Cp* at the location of non-dimensional meridional distancemm, and the horizontal axis represents a specific need Ns of theturbomachinery. Data plotted on the plane defined by both axes are thesame as the data plotted on the plane of FIGS. 4 and 5. A boundary lineof negatively sloped straight line can be drawn so that data shown byopen symbols representing adaptation to the quantitative criterion ofjudgement about suppression of the secondary flow are located on thedata area at the upper right of the drawing, and data shown by solidsymbols representing nonadaptation to the quantitative criterion ofjudgement about suppression of the secondary flow are located on thedata area at the lower left of the drawing.

By reading the gradient of the boundary line, and the intersection ofthe boundary line and the vertical axis, as a function which isdependent on the specific speed Ns and represents the difference D* ofthe normalized reduced static pressure difference, the appropriatenessof the following equation was confirmed.

    D*=.increment.Cp*m-0.4-.increment.Cp*m=-0.004 Ns+3.62

where the normalized pressure coefficient is defined in the followingequation.

    Cp*=Cp/Cp, mid-mid

where Cp, mid-mid is a pressure coefficient in the center of the flowchannel as shown in FIG. 1(D).

In compressors which handle compressive fluid, the relative Mach numberM can be related to the pressure coefficient Cp by the followingequation, thus the normalized pressure coefficient Cp* is applicable toevery kinds of fluid.

    Cp=2[1-(1-0.5W.sup.2 /H.sub.0 *).sup.γ/(γ-1) ]/γM.sub.0 *.sup.2

    M.sub.0 *=Ut/(γP.sub.0 */ρ.sub.0 *).sup.0.5

where Ut is a peripheral speed of the impeller, W is a relativevelocity, H₀ * is a rothalpy, γ is a ratio of specific heats, P₀ * is arotary stagnation pressure, and ρ₀ * is a density corresponding to P₀ *.

In verification examples, the differences(D*=.increment.Cp*m-0.4-.increment.Cp*m) of the reduced static pressuredifferences, which are the basis of the values of the data plotted onthe plain of FIG. 6, are shown in a table of FIG. 7(B).

Incidentally, verification examples 7 and 8 are related to the pumps ofa specific speed Ns=377. It was confirmed that the data of the aboveverification examples are defined by the boundary line on the plane ofFIG. 6, and located on the data area of nonadaptation to suppression ofthe secondary flow. Incidentally, it is confirmed by thethree-dimensional viscous calculations that the value of pressurecoefficient slope at the shroud side which is negative and extremelysmall (steep), compared with the lower limit of the pressure coefficientslope at the shroud side CPS-s,_(LIM), emerges in the fore part towardthe impeller inlet (m=0) from the location of non-dimensional meridionaldistance m-0.4, therefore flow separation is generated in the fore partof the impeller. Therefore, the information on the secondary flowdevelopment in the verification data of 7 and 8 could not beascertained.

An embodiment according to the third and fourth aspects of the presentinvention will be described below. When designing and manufacturing aturbomachinery having an impeller with a three-dimensional shape forrealizing the remarkably decreasing tendency in the reduced staticpressure difference .increment.Cp or the relative Mach number difference.increment.M characterized by the first aspect of the present inventionalong the location of non-dimensional meridional distance m toward theimpeller exit in the third aspect of the present invention, and whendesigning and manufacturing a turbomachinery having an impeller with athree-dimensional shape for realizing the remarkably decreasing tendencyin the reduced static pressure difference .increment.Cp* characterizedby the second aspect of the present invention on the basis of thenormalized pressure coefficient Cp*, the following design method for thethree-dimensional geometry of the impeller is utilized. The designmethod comprises a first step of determining the meridional geometry, asecond step of determining the blade loading distribution, a third stepof determining blade profile, a fourth step of judging the optimumreduced static pressure difference .increment.Cp and the like, and afifth step of evaluating flow fields.

In these aspects, while selecting properly by trial and error the bladeloading distribution on the basis of the known close relationshipbetween the pressure coefficient Cp and the angular momentum rV.sub.θ,the pressure coefficient Cp is increased or decreased. And, by utilizingthe following three-dimensional inverse design method using the rV.sub.θdistribution as an input data, the three-dimensional shape of theimpeller which realizes a characteristic distribution characterized bythe first and second aspects of the present invention is determined.

In this case, the design method is processed by the flow chart shown inFIG. 3(B).

In the first step (step of determining meridional geometry), based onthe conventional knowledge about the correlation with the specific speedNs calculated from the design specification, the meridional shape of thehub and the shroud and the position of the leading edge of the blade andthe trailing edge of the blade are defined, and the number of blades ofthe impeller is selected. Mesh required for numerical calculation isformed at equal intervals or unequal intervals along the hub and theshroud surfaces. This mesh is extended to upstream of the leading edgeof the blade and downstream of the trailing edge of the blade. The meshis similar to that in FIG. 1(C) of the mesh for viscous flowcalculations. Quasi-Orthogonal lines (Q-O line) are drawn by connectingthe corresponding points on the hub and the shroud. Next, a plurality ofsurfaces of revolution is defined in the meridional flow channel, andthe stacking condition f₀ (tangential co-ordinate of the blade camberline at a point on each of surfaces of revolution). The process in thefirst step is essentially the same as the process in the first step ofthe conventional design method shown in FIG. 3(A).

In the second step (step of determining blade loading distribution), theshape of the blade loading distribution ∂(rV.sub.θ)/∂m is selected sothat the blade loading distribution has a peak on the shroud surface inthe first half of the non-dimensional meridional distance m along theshroud and a peak on the hub surface in the latter half of thenon-dimensional meridional distance m along the hub. Next, thedistribution of ∂(rV.sub.θ)/∂m along the hub and shroud is integratedalong the non-dimensional meridional distance m to determine rV.sub.θdistribution. The resultant values on the hub and the shroud surfacesobtained by integration along the non-dimensional meridional distance mare adjusted to satisfy the exit velocity triangles (i.e. the V.sub.θvalues on the hub and the shroud at the impeller exit determined, inmanner similar to the conventional method, from the design head of theimpeller), and the rV.sub.θ distribution between the hub and the shroudis determined by the linear interpolation along Q-O line determined bythe first step.

In the third step (step of determining blade profile), the blade camberline is obtained by applying the condition that the velocity is alongthe blade at the blade camber line, i.e. there is no flow through theblade camber.

If we represent the location of the blade camber line α, which isdefined as:

    α=θ-f(r, z)=0, n2π/B, (n=1, 2, 3 . . . B)

where f is the tangential co-ordinate of the blade camber line (or wrapangle), θ is the tangential co-ordinate of cylindrical polar co-ordinatesystem, and B is the number of blades (as shown in FIG. 1(E)).

The above condition is expressed mathematically in the followingequation.

    W-·∇(α)=0, W-·∇(α)=0

where W· and W- are the relative velocities of the pressure and thesuction surfaces of the blade, respectively, ∇ is vector calculusoperator.

The above two equations are combined to give the following equation.

    W.sub.b1 ·∇α=0 where W.sub.b1 =(W·+W-)/2

The above equation can be decomposed into its components and expressedin the following equation.

    {(Vz+v.sub.zb1)∂f/∂z}+{(Vr+v.sub.rb1).differential.f/∂r}={(rV.sub.θ)/r.sup.2 }+{(v.sub.θb1)/r}-ω

The above equation is a first order hyperbolic partial differentialequation. The value of f₀ along an arbitrary Q-O line in the blade (thestacking condition) is used as an initial value, and the above equationis integrated along the non-dimensional meridional distance m, and thetangential co-ordinate of the blade camber line f in the location ofnon-dimensional meridional distance m is determined. And, thethree-dimensional geometry of the impeller is determined by adding acertain thickness to the determined blade camber line to allow the bladeto have required mechanical strength. The stacking condition can bespecified by, for example, setting the zero value of f₀ along the Q-Oline at the blade trailing edge, or setting a moderate distribution off₀ value along the Q-O line at the blade trailing edge.

The calculation of the relative velocity W, in the above mentionedequations, is processed in the following manner.

The velocity field is split into tangentially-averaged and tangentiallyperiodic components. To determine the tangentially-averaged flow theradial and axial velocities (Vr and Vz, respectively) are expressed interms of a stream function in order to satisfy the continuity (or massconservation) equation of fluid dynamics. Then a Poisson type partialdifferential equation governing the stream function is obtained by usinga suitable equation for the vorticity field generated by the action ofthe blades, which in turn is related to the blade circulation2πrV.sub.θ. This equation can then be integrated by any suitablenumerical method subject to uniform velocity conditions at upstream anddownstream boundaries and no flow (or constant stream function)conditions at the hub and shroud walls. Integration of this equationwill give the values of stream function from which Vr and Vz areobtained.

The velocity terms v_(rb1), v_(zb1) and v.sub.θb1 are obtained from thesolution of the tangentially periodic flow. For the solution of theperiodic flow the Clebsch formulation of the velocity field is used. Inthis formulation the velocity field is split into an unknownirrotational part (represented by a velocity potential function) and aknown rotational part which is related to the blade circulation2πrV.sub.θ. The governing equation of the unknown potential function isthen found by using the Clebsch formulation for the velocity field inthe continuity equation of the periodic flow. In this way a 3D Poisson'sequation is obtained which can then be integrated by a suitablenumerical technique, subject to vanishing periodic tangential velocityand spanwise velocity at upstream and downstream boundaries and no-flowconditions through the hub and shroud surface.

According to the above method, velocity field as well as blade loadingof the impeller, i.e. the pressure difference p(+)-p(-) between thepressure p(+) on the pressure surface and the pressure p(-) on thesuction surface of the blade can be obtained in the following equation.

    {p(+)-p(-)}/ρ=2π(W.sub.b1 ·∇rV.sub.θ)/B,

where W_(b1) is relative velocity at the location on blade surface.

In this way, the reduced static pressure difference .increment.Cp or therelative Mach number difference .increment.M between the hub and theshroud on the suction surface of the blade can be obtained.

Further, the value which is not dependent on the specific speed and thetype of the impeller, i.e. both for a compressor which handlescompressible fluid and a pump which handles incompressible fluid, thenormalized pressure coefficient Cp* is defined as follows.

    Cp*=Cp/Cp,mid-mid

where Cp,mid-mid is the pressure coefficient at the center of the flowchannel (midspan and midpitch) at the location of non-dimensionalmeridional distance m. The pressure coefficient Cp in compressible fluidis defined in the following equation.

    Cp*=2[1-(1-0.5W.sup.2 /H.sub.0 *).sup.γ/(γ-1) ]/γM.sub.0 *.sup.2

    M.sub.0 *.sup.2 =Ut/(γP.sub.0 */ρ.sub.0 *).sup.0.5

where Ut is a peripheral speed of the impeller, W is a relativevelocity, H₀ * is a rothalpy, γ is a ratio of specific heats, P₀ * is arotary stagnation pressure, and ρ₀ * is a density corresponding to P₀ *.

In the fourth step (a step of judging optimum reduced static pressuredifference .increment.Cp and the like), it is judged whether or not thedistribution of the reduced static pressure difference .increment.Cp orthe relative Mach number difference .increment.M along the location ofnon-dimensional meridional distance m calculated in the third step issuitable for suppression of the secondary flow in the impeller. Whenestablishing the distribution of reduced static pressure difference.increment.Cp for realizing suppression of the secondary flow, thedecreasing tendency in the reduced static pressure difference.increment.Cp is realized by (a) the degree of dependence on a variationat the shroud side, (b) the degree of dependence on a variation at thehub side, and (c) the degree of dependence on both variation at theshroud side and the hub side. In order to judge the suitable.increment.Cp distribution numerically, the pressure coefficient slopeon the suction surface of the blade at the shroud side CPS-s and thepressure coefficient slope on the suction surface of the blade at thehub side CPS-h between the location of a minimum value .increment.Cpm ofthe reduced static pressure difference .increment.Cp and the location ofnon-dimensional meridional distance mm-0.4 obtained by subtractingnon-dimensional meridional distance 0.4 from non-dimensional meridionaldistance mm representing the minimum value .increment.Cpm are defined,and it is judged whether this value satisfies the criteria defined inthe first aspect of the present invention. In the case where thevariation of .increment.Cp is largely dependent on the variation of theshroud side, and the pressure distribution becomes such that anexcessive pressure increase (or excessive deceleration of the relativevelocity) occurs, a great amount of flow separation occurs at the samearea generating lower head, poor efficiency or decrease in operationalrange. Therefore, care should be taken so as not to cause suchdistribution based on the CPS-s,_(Lim) limit defined in the first aspectof the present invention.

Incidentally, in the case of incompressible fluid, the pressurecoefficient Cp is equal to (W/U)², where W is relative velocity. Incompressible fluid as in compressors, the physical variable related tothe behavior of secondary flow is relative Mach number. Therefore, inthe case of compressible fluid, the same judgement concerning thereduced static pressure difference ΔCp is applied to the relative Machnumber difference ΔM based on the criteria defined in the first aspectof the present invention.

Further, by using the normalized pressure coefficient Cp* proposed fordesign criterion of secondary flow suppression as common designcriterion concerning pumps and compressors, it is possible to judge fromthe difference between a minimum value ΔCp*m of the normalized reducedstatic pressure difference ΔCp* and a value ΔCp*_(m-0).4 of thenormalized reduced static pressure difference ΔCp* at the locationcorresponding to non-dimensional meridional distance mm-0.4 obtained bysubtracting non-dimensional meridional distance 0.4 from non-dimensionalmeridional distance mm representing the minimum value ΔCpm.

By the above manner, it is judged whether the optimum reduced staticpressure difference can be obtained, if it is not satisfied, after goingback to the second step to modify the blade loading distribution, thesteps from the second step to the above steps are repeated until theoptimum reduced static pressure difference is obtained. After completingthis step, the blade loading distribution ∂(rV.sub.θ)/∂m in whichoptimum reduced pressure distribution can be obtained is determined. Asa result, in the design of an impeller having similar designspecifications, the above mentioned optimum distribution of the bladeloading ∂(rV.sub.θ)/∂m is applicable, and the optimization process forthe new design can be greatly accelerated.

In the fifth step (step of evaluation of flow fields), a possibility ofpoor performance caused by the flow separation due to rapid decelerationor rapid pressure increase in the impeller determined by the third stepis evaluated. In the case where it is judged that the pressuredistribution in the impeller is not appropriate, after going back to thesecond step to modify the blade loading distribution, the steps from thesecond step to the fifth step are repeated until the expected result isachieved.

In the second step of the third and fourth aspects of the presentinvention, the characteristics of flow fields, i.e. the blade loadingdistribution directly related to the flow physics, is used as input datafor the third step to determine the blade profile, therefore the bladeprofile for suppressing the secondary flow can be promptly designed andan impeller having such blade profile can be easily manufactured,compared with the conventional manufacturing method using themodification of blade angle distribution by trial and error.

Incidentally, concerning the method in the third step to obtain theblade profile based on the specified rV.sub.θ distribution determined inthe second step, other inverse design methods including the effects ofthe finite blade thickness on the velocity fields or semi-inversemethods such as Soulis, J. V., 1985, "Thin Turbomachinery Blade DesignUsing A Finite-Volume Method", International Journal of NumericalMethods in Engineering, vol. 21, p. 19, which are based on iterativeapplication of analysis methods, are available, However, these methodsrequire more computational time and are less efficient compared withthat described in the third step of the third and fourth aspects of thepresent invention.

According to the present invention, there is provided a turbomachineryhaving an impeller, characterized in that the impeller is designed sothat the reduced static pressure difference ΔCp or the relative Machnumber difference ΔM between the hub and the shroud on the suctionsurface of a blade shows a remarkably decreasing tendency along thelocation of non-dimensional meridional distance m toward the impellerexit.

(1) In order to obtain the above remarkably decreasing tendency, theblade profile of the impeller is determined by utilizing thethree-dimensional inverse design method using the blade loadingdistribution as input data so that the difference D between a minimumvalue ΔCpm of the reduced static pressure difference ΔCp and a valueΔCp_(m-0).4 of the reduced static pressure difference ΔCp at thelocation corresponding to non-dimensional meridional distance mm-0.4obtained by subtracting non-dimensional meridional distance 0.4 fromnon-dimensional meridional distance mm representing the above minimumvalue ΔCpm is selected to be a specified value which is dependent on aspecific speed of the turbomachinery. Further, the difference DM betweena minimum value ΔMm of the relative Mach number difference ΔM and avalue ΔM_(m-0).4 of the relative Mach number difference ΔM at thelocation corresponding to the above non-dimensional meridional distancemm-0.4 is also selected to be a specified value which is dependent on aspecific speed of the turbomachinery.

(2) Instead of the pressure coefficient Cp or the Mach number M, andthus the reduced static pressure difference ΔCp or the relative Machnumber difference ΔM, the normalized pressure coefficient Cp* iscommonly used for compressible fluid and incompressible fluid so thatthe normalized pressure coefficient difference D* corresponding to theabove difference D or DM is expressed as a function of the specificspeed Ns. Then, the blade profile of the impeller is determined byutilizing the three-dimensional inverse design method using the bladeloading distribution as input data so that the above difference D*corresponding to the turbomachinery of a given specific speed isselected to be a specified value which complies with the above function.

(3) The turbomachinery is designed and manufactured by utilizing thethree-dimensional inverse design method using the aspects characterizedby the above (1) and (2) as input data.

With regard to the above-described aspects (1)-(3), whose propriety issubstantiated by a large amount of verification data, therefore thepresent invention can be utilized effectively in industry.

According to the above aspects, since the meridional component ofsecondary flow can be effectively suppressed, a loss which occurs in theturbomachinery or the downstream flow channel can be reduced, emergenceof a positively sloped characteristic curve can be avoided, andstability of operation can be improved. Therefore, the present inventionhas a great utility value in industry.

We claim:
 1. A turbomachine having an impeller with a plurality ofblades supported by a hub on which said blades are circumferentiallyspaced and covered by a shroud surface which forms an outer boundary toflow of fluid in a flow passage defining a flow direction between twoadjacent blades, characterized in that:said impeller has a configurationsuch that one of a reduced static pressure difference ΔCp and a relativeMach number difference ΔM between the hub and the shroud on the suctionsurface of the blade shows a decreasing tendency along the location ofnon-dimensional meridional distance m toward the impeller exit and isselected to be not less than a specified value which is dependent on aspecific speed Ns of the turbomachines, herein specific speed Ns isdefined as Ns=NQ⁰.5 /H⁰.75, where N is the rotational speed inrevolution per minutes, Q is the flow rate at an impeller inlet in cubicmeter per minutes, and H is the head in meter representing fluid energywhich is imparted to the fluid by the turbomachine; said decreasingtendency of ΔCp for the turbomachine handling incompressible fluid isarranged such that the reduced static pressure difference between aminimum value ΔCpm of reduced static pressure difference ΔCp and a valueΔCp_(m-0).4 of reduced static pressure difference ΔCp at the locationcorresponding to non-dimensional meridional distance M_(m-0).4 obtainedby subtracting non-dimensional meridional distance 0.4 fromnon-dimensional meridional distance M_(m) representing said minimumvalue ΔCpm is selected to be not less than 0.20 at said specific speedNs of not more than 280, not less than 0.28 at said specific speed Ns ofnot more than 400, and not less than 0.35 at said specific speed Ns ofnot more than 560; and said decreasing tendency of ΔM for theturbomachine handling compressible fluid is arranged such that relativeMach number difference between a minimum value ΔMm of the relative Machnumber difference ΔM and a value ΔM_(m-0).4 of the relative Mach numberdifference ΔM at the location corresponding to non-dimensionalmeridional distance M_(m-0).4 obtained by subtracting non-dimensionalmeridional distance 0.4 from non-dimensional meridional distance M_(m)representing said minimum value ΔMm is selected to be not less than 0.23at said specific speed of not more than
 488. 2. The turbomachine asrecited in claim 1, wherein the non-dimensional meridional distanceM_(m) representing said minimum value ΔCpm of the reduced staticpressure difference ΔCp is selected to be in the range ofnon-dimensional meridional distance m=0.8-1.0.
 3. The turbomachine asrecited in claim 1 or 2, wherein a pressure coefficient slope at theshroud side CPS-s on the suction surface of the blade is selected to benot less than -1.3 as a lower limit of the pressure coefficient slope atthe shroud side CPS-s,_(Lim).
 4. The turbomachine as recited in claim 1,wherein a Mach number slope at the shroud side Ms-s on the suctionsurface of the blade is selected to be not less than -0.8 as a lowerlimit of the Mach number slope at the shroud side MS-s,_(Lim).
 5. Theturbomachine as recited in claim 1 or 4, wherein the non-dimensionalmeridional distance M_(m) representing said minimum value ΔM of therelative Mach number difference ΔM is selected to be in the range ofnon-dimensional meridional distance m=0.8-1.0.
 6. A turbomachine havingan impeller with a plurality of blades supported by a hub on which saidblades are circumferentially spaced and covered by a shroud surfacewhich forms an outer boundary to flow of fluid in a flow passagedefining a flow direction between two adjacent blades, characterized inthat:said impeller has a configuration such that normalized reducedstatic pressure difference ΔCp* between the hub and the shroud on thesuction surface of a blade shows a remarkably decreasing tendency alongthe location of non-dimensional meridional distance m toward theimpeller exit, and said remarkably decreasing tendency is arranged suchthat the difference D* between a minimum value ΔCp*m of the reducedstatic pressure difference ΔCp* and a value ΔCp*_(m-0).4 of the reducedstatic pressure difference ΔCp* at the location corresponding tonon-dimensional meridional distance M_(m-0).4 obtained by subtractingnon-dimensional meridional distance 0.4 from non-dimensional meridionaldistance m_(m) representing said minimum value ΔCp*_(m) is selected tobe not less than D*=-0.004Ns+3.62, herein specific speed Ns is definedas Ns=NQ⁰.5 /H⁰.75, where N is the rotational speed in revolution perminutes, Q is the flow rate at an impeller inlet in cubic meter perminutes, and H is the head in meter representing fluid energy which isimparted to the fluid by the turbomachine.
 7. A method of manufacturinga turbomachine having an impeller with a plurality of blades supportedby a hub on which said blades are circumferentially spaced and coveredby a shroud surface which forms an outer boundary to flow of fluid in aflow passage defining a flow direction between tow adjacent blades,comprising:a first step of selecting meridional geometry and the numberof blades of the impeller using design specification as input data,defining a plurality of surface of revolution in a meridional flowchannel, and determining stacking condition f₀ ; a second step ofdetermining distribution of blade loading rV.sub.θ along non-dimensionalmeridional distance m by selecting a shape of the blade loadingdistribution ∂(rV.sub.θ)/∂m which has a peak on the shroud surface inthe first half of the location of non-meridional distance m and a peakon the hub surface in the latter half of the location of non-dimensionalmeridional distance m, adjusting a value obtained by integrating theblade loading distribution along the non-dimensional meridional distancem so as to satisfy design head of the impeller; a third step ofdetermining three-dimensional geometry of the impeller by integrating

    {(Vz+V.sub.zb1)∂f/∂z}+{(Vr+V.sub.rb1).differential.f/∂r}={(rV.sub.074 )/r.sup.2 }+{(V.sub.θb1)/r}-ω

along non-dimensional meridional distance m using stacking condition ∫₀as initial value to determine tangential co-ordinate f of the bladecamber line in non-dimensional meridional distance m and adding acertain thickness to the determined value to allow the blade to haverequired mechanical strength; a fourth step of judging whether one ofthe distribution of reduced static pressure difference ΔCp and thedistribution of a relative Mach number difference ΔM alongnon-dimensional meridional distance m obtained by the third step issuitable for suppressing the secondary flow in the impeller or not; afifth step of evaluating possibility of poor performance caused by atleast flow separation in the impeller determined by the third step,evaluating secondary flow in the impeller by a secondary flow parameter,and after going back to the second step to modify the blade loadingdistribution on the basis of the above evaluations, repeating the abovesteps until the expected result is achieved; wherein one of a reducedstatic pressure difference ΔCp and a relative Mach number difference ΔMbetween the hub and the shroud on the suction surface of the blade showsa remarkably decreasing tendency along the location of non-dimensionalmeridional distance m toward the impeller exit and is selected to be notless than a specified value which is dependent on a specific speed Ns ofthe turbomachines, herein specific speed Ns is defined as Ns=NQ⁰.5/H⁰.75, where N is the rotational speed in revolution per minutes, Q isthe flow rate at an impeller inlet in cubic meter per minutes, and H isthe head in meter representing fluid energy which is imparted to thefluid by the turbomachine; said remarkably decreasing tendency of ΔCpfor the turbomachine handling incompressible fluid is arrange such thatthe reduced static pressure difference between a minimum value ΔCpm ofreduced static pressure difference ΔCp and a value ΔCp_(m-0).4 ofreduced static pressure difference ΔCp at the location corresponding tonon-dimensional meridional distance M_(m-0).4 obtained by subtractingnon-dimensional meridional distance 0.4 from non-dimensional meridionaldistance M_(m) representing said minimum value ΔCpm is selected to benot less than 0.20 at said specific speed Ns of not more than 280, notless than 0.28 at said specific speed Ns of not more than 400, and notless than 0.35 at said specific speed Ns of not more than 560; and saidremarkably decreasing tendency of ΔM for the turbomachine handlingcompressible fluid is arranged such that relative Mach number differencebetween a minimum value ΔM of the relative Mach number difference ΔM anda value ΔM_(m-0).4 of the relative Mach number difference ΔM at thelocation corresponding to non-dimensional meridional distance M_(m-0).4obtained by subtracting non-dimensional meridional distance 0.4 fromnon-dimensional meridional distance M_(m) representing said minimumvalue ΔMm is selected to be not less than 0.23 at said specific speed ofnot more than
 488. 8. The method of manufacturing the turbomachine asrecited in claim 7, wherein it is judged whether the non-dimensionalmeridional distance M_(m) representing said minimum value ΔCpm of thereduced static pressure difference ΔCp is in the range ofnon-dimensional meridional distance m=0.8-1.0 or not.
 9. The method ofmanufacturing the turbomachine as recited in claim 7 or 8, wherein it isjudged whether pressure coefficient slope at the shroud side CPS-s onthe suction surface of the blade is not less than -1.3 as a lower limitof the pressure coefficient slope at the shroud side CPS-s,_(Lim). 10.The method of manufacturing the turbomachine as recited in claim 7,wherein it is judged whether the Mach number slope at the shroud sideMs-s on the suction surface of the blade is not less than -0.8 as alower limit of the Mach number slope at the shroud side MS-s,_(Lim). 11.The method of manufacturing the turbomachine as recited in claim 7 or10, wherein it is judged whether the non-dimensional meridional distancem_(m) representing said minimum value ΔMm of the relative Mach numberdifference ΔM is in the range of non-dimensional meridional distancem=0.8-1.0.
 12. A method of manufacturing a turbomachine having animpeller with a plurality of blades supported by a hub on which saidblades are circumferentially spaced and covered by a shroud surfacewhich forms an outer boundary to flow of fluid in a flow passagedefining a flow direction between two adjacent blades, comprising:afirst step of selecting meridional geometry and the number of blades ofthe impeller using design specification as input data, defining aplurality of surfaces of revolution in a meridional flow channel, anddetermining stacking condition ∫₀ ; a second step of determiningdistribution of blade loading rV.sub.θ along non-dimensional meridionaldistance m by selecting a shape of the blade loading distribution∂(rV.sub.θ)/∂m which has a peak on the shroud surface in the first halfof the location of non-dimensional meridional distance m and a peak onthe hub surface in the latter half of the location on non-dimensionalmeridional distance m, adjusting a value obtained by integrating theblade loading distribution along the non-dimensional meridional distanceme so as to satisfy design head of the impeller; a third step ofdetermining three-dimensional geometry of the impeller by integrating

    {(Vz+V.sub.zb1)∂f/∂z}+{(Vr+V.sub.rb1).differential.f/∂r}={(rV.sub.θ)/r.sup.2 }+{(V.sub.θb1)/r}-ω

along non-dimensional meridional distance m using stacking condition f₀as initial value to determine tangential co-ordinate f of the bladechamber line in non-dimensional meridional distance m and adding acertain thickness to the determined value to allow the blade to haverequired mechanical strength; a fourth step of judging whether thedistribution of normalized reduced static pressure difference ΔCp* alongnon-dimensional meridional distance m obtained by the third step issuitable for suppressing the secondary flow in the impeller or not; anda fifth step of evaluating possibility of poor performance caused by atleast flow separation in the impeller determined by the third step,evaluating secondary flow in the impeller by a secondary flow parameter,and after going back to the second step to modify the blade loadingdistribution on the basis of the above evaluations, repeating the abovesteps until the expected result is achieved; wherein normalized reducedstatic pressure difference ΔCp* between the hub and the shroud on thesuction surface of a blade shows a remarkably decreasing tendency alongthe location of non-dimensional meridional distance m toward theimpeller exit, and said remarkably decreasing tendency is judged by thefourth step whether the difference D* between a minimum value ΔCp*m ofthe reduced static pressure difference ΔCp* at the locationcorresponding to non-dimensional meridional distance M_(m-0).4 obtainedby subtracting non-dimensional meridional distance 0.4 fromnon-dimensional meridional distance M_(m) representing said minimumvalue ΔCp*m is not less than D*=-0.004Ns+3.62, herein specific speed Nsis defined as Ns=NQ⁰.5 /H⁰.75, where N is the rotational speed inrevolution per minutes, Q is the flow rate at an impeller inlet in cubicmeter per minutes, and H is the head in meter representing fluid energywhich is imparted to the fluid by the turbomachine.